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OO development was being done long before modeling tools existed. The modeling tools were created as a way to assist OO development. Whether or not they have really succeeded in making OO development easier is the subject of a different question.

For that matter, you can perform OO like development in non-OO languages. It's difficult to simulate inheritance and polymorphism without language support, but the aspects of encapsulation and information hiding don't require specific OO language constructs.

Is it true that Object Orinted programming can be done without any specific modelling like OMT.

OOP is a way to program - Modeling is a way to facilitate thinking and documentation of specifications and requirements of a system. Object Modeling is a modeling type that focuses on modeling techniques using Objects.

What are the models available for object Oriented software development?

OOP is often modeled via Unified Modeling Language (UML). However, UML is a specification not a methodology, it does not tell you what to do. UML is not required to create working OO programs.

OOP practitioners and theorists have collected and presented some useful experiences for common programming situations in what is referred to as patterns (see for example: Wiki-Design Patterns.